Nuprl Lemma : rotate-inverse1
∀[n:ℕ+]. ((rot(n) o rot(n)^n - 1) = (λx.x) ∈ (ℕn ⟶ ℕn))
Proof
Definitions occuring in Statement : 
rotate: rot(n)
, 
fun_exp: f^n
, 
compose: f o g
, 
int_seg: {i..j-}
, 
nat_plus: ℕ+
, 
uall: ∀[x:A]. B[x]
, 
lambda: λx.A[x]
, 
function: x:A ⟶ B[x]
, 
subtract: n - m
, 
natural_number: $n
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
compose: f o g
, 
member: t ∈ T
, 
top: Top
, 
nat: ℕ
, 
nat_plus: ℕ+
, 
guard: {T}
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
all: ∀x:A. B[x]
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
prop: ℙ
, 
true: True
, 
squash: ↓T
, 
subtype_rel: A ⊆r B
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
Lemmas referenced : 
fun_exp_add1, 
subtract_wf, 
int_seg_properties, 
nat_plus_properties, 
decidable__le, 
satisfiable-full-omega-tt, 
intformand_wf, 
intformnot_wf, 
intformle_wf, 
itermConstant_wf, 
itermSubtract_wf, 
itermVar_wf, 
intformless_wf, 
int_formula_prop_and_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_subtract_lemma, 
int_term_value_var_lemma, 
int_formula_prop_less_lemma, 
int_formula_prop_wf, 
le_wf, 
subtract-add-cancel, 
int_seg_wf, 
nat_plus_wf, 
equal_wf, 
rotate-order, 
iff_weakening_equal
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
cut, 
functionExtensionality, 
sqequalRule, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
dependent_set_memberEquality, 
setElimination, 
rename, 
hypothesisEquality, 
hypothesis, 
natural_numberEquality, 
because_Cache, 
productElimination, 
dependent_functionElimination, 
unionElimination, 
independent_isectElimination, 
dependent_pairFormation, 
lambdaEquality, 
int_eqEquality, 
intEquality, 
independent_pairFormation, 
computeAll, 
applyEquality, 
imageElimination, 
imageMemberEquality, 
baseClosed, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}].  ((rot(n)  o  rot(n)\^{}n  -  1)  =  (\mlambda{}x.x))
Date html generated:
2017_04_17-AM-08_08_49
Last ObjectModification:
2017_02_27-PM-04_36_20
Theory : list_1
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